Analysis of Two-Dimensional Cavity Flow by Finite Elements

Lin Bin-yao; Xu Xie-qing

Volume 6 Issue 5

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(5): 465-474

Lin Bin-yao, Xu Xie-qing. Analysis of Two-Dimensional Cavity Flow by Finite Elements[J]. Applied Mathematics and Mechanics, 1985, 6(5): 465-474.

Citation:

Lin Bin-yao, Xu Xie-qing. Analysis of Two-Dimensional Cavity Flow by Finite Elements[J]. Applied Mathematics and Mechanics, 1985, 6(5): 465-474.

Citation:

Lin Bin-yao, Xu Xie-qing. Analysis of Two-Dimensional Cavity Flow by Finite Elements[J]. Applied Mathematics and Mechanics, 1985, 6(5): 465-474.

PDF( 592 KB)

Analysis of Two-Dimensional Cavity Flow by Finite Elements

Lin Bin-yao¹,
Xu Xie-qing²

1.
Institute of Water Conservancy and Hydroelectric Power Research, Beijing;
2.
Institute of Water Conservancy and Hydroelectric Power Research, Qinghua University, Beijing

Received Date: 1982-08-09
Publish Date: 1985-05-15

Abstract

Abstract

The variational principle in terms of stream function ψ for free surface gravity flow is discussed by the formulation of first-order variation in a variable domain. Because of different transversal conditions adopted, there are four forms of variational principle in terms of ψ.An air-gilled cavity flow with given discharge and total energy is then analysed by finite element method. At the end of the cavity, the free stream line is tangent to a short fictitious plate of given length, which joins the fixed boundary at on angle to be determined. The condition that the free stream line should be tangent to the fixed boundary at the point of separation makes the solution unique.Finally curves giving the cavity length as a function of the Fraude number, cavity pressure and channel bottom slope are presented.

FullText(HTML)

References(9)

References

[1]	Wu,Th,y-t.(吴耀祖),Cavity and wake flows,Annual Review of Fluid Mechanics,4.(1972).
[2]	Ikegawa,M.,K.Washizu,Finite element method applied to analysis of flow over a spillway crest,Inter,J.of Num.Mech.in Eng.,6(1973).
[3]	水电部水利调度研究所,乌江渡水电站右岸泄洪洞溢流面压力分布的有限元法计算,1(1976年1月)
[4]	许协庆,自由面重力流的一种有限元解法.水利学报.1(1980).
[5]	Yaroglu,E,and W,D,Liam Finn,YariabIe domain finite element analysis of free-surface gravity flow,Computer and Fluids.,6(1978).
[6]	Betts,P,L.,A variational principle in.' terms of stream functioa for free-surface flows and its application to the finite element method,Computer and Fluids,7(1979).
[7]	柯朗、希尔伯特,《数学物理方法》,I,科学出版社,(1958).
[8]	许协庆、周胜.圆弧弓形和半弓形突体绕流的压力分布和初生空穴数,水利水电科学研究院论文集,(1964年).
[9]	Knapp,R,T.,7.W.Daily and F.G,Hammitt,Cavitation,(1970).

Relative Articles

[1]	DUAN Xiaoyu, MA Yongbin. Effects of the Gravity Field on 2D Fiber-Reinforced Media Under the Fractional Order Theory of Thermoelasticity[J]. Applied Mathematics and Mechanics, 2021, 42(5): 452-459. doi: 10.21656/1000-0887.410125
[2]	TANG Yi-jun, LUO Jian-hui. Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode[J]. Applied Mathematics and Mechanics, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005
[3]	YANG Yong-qin, XIAO Liu-chao, CHEN Shao-chun. Nonconforming Finite Elements for the Equation of Planar Elasticity[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1454-1464. doi: 10.3879/j.issn.1000-0887.2010.12.006
[4]	JIN Jian-ming, XUE Peng-xiang, XU Ying-xiang, ZHU Ya-li. Compactly Supported Non-Tensor Product Form Two Dimension Wavelet Finite Element[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1464-1476.
[5]	QIN Xin-qiang, MA Yi-chen, ZHANG Yin. Two-Grid Method for Characteristics Finite-Element Solution of 2D Nonlinear Convection-Dominated Diffusion Problem[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1365-1372.
[6]	Zhu Jufen, Zheng Gang, Wu Jinying. F.E.M. Analysis of Delamination Buckling in Composite Plates & Shells[J]. Applied Mathematics and Mechanics, 2000, 21(3): 301-306.
[7]	Yan Bo, Liu Zhanfang, Zhang Xiangwei. Finite Element Analysis of Wave Propagation in Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1235-1244.
[8]	Zhang Jianhai, Chen Dapeng, Zou Shengquan. ALE Finite Element Analysis of the Opening and Closing Process of the Artificial Mechanical Valve[J]. Applied Mathematics and Mechanics, 1996, 17(5): 387-396.
[9]	Zhang Hong-wu, Zhong Wan-xie, Qian Ling-xi. Finite Element Analysis for Consolidation in Interaction between Structure and Saturated Soil Foundation[J]. Applied Mathematics and Mechanics, 1992, 13(10): 891-899.
[10]	Li Long-yuan. The Rationalism Theory and Its Finite Element Analysis Method of Shell Structures[J]. Applied Mathematics and Mechanics, 1990, 11(4): 365-372.
[11]	Chen Da-peng, Zhao Zhong. A Penalty-Hybrid Finite Element Analysis of Stokes Flow[J]. Applied Mathematics and Mechanics, 1990, 11(6): 467-476.
[12]	Chen Xiao-ming, Guan Zhong-xin, Zhuang Jia-lin. Analysis to the Stress Construction at the Vicinity of Crack Tip for Mode I Fracture in 3-D State Using Finite Element Method[J]. Applied Mathematics and Mechanics, 1988, 9(6): 559-566.
[13]	Qian Yuan-yao. A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates[J]. Applied Mathematics and Mechanics, 1987, 8(8): 733-742.
[14]	Zhang Shuang-yin, C. M. Leech. FEM Analysis on Mixed-Mode Fracture of CSM-GRP[J]. Applied Mathematics and Mechanics, 1986, 7(8): 689-702.
[15]	S. N. Atluri, Kuang Zhen-bang. A Finite Element Analysis for the Temperature Field Produced by a Moving Heat Source[J]. Applied Mathematics and Mechanics, 1986, 7(5): 383-400.
[16]	Su Ming-de. Finite Element Analysis of Non-Newtonian Fluid Flow in 2-D Branching Channel[J]. Applied Mathematics and Mechanics, 1986, 7(10): 929-936.
[17]	Liu Zheng-xing, Wu Lian-yuan, Feng Tai-hua. The Finite Element Analysis of the Flexible Beams and Plates[J]. Applied Mathematics and Mechanics, 1985, 6(9): 833-844.
[18]	Lü Yu-lin, Lai Guo-zhang. The Mathematical Modelling of Near Coast Shallow Water Circulation[J]. Applied Mathematics and Mechanics, 1984, 5(5): 731-742.
[19]	He Qiong, Cheng Zheng-ding, Xiong Huan-guo. Finite Element Study of Dynamic Characteristics of Main Components of Machine Tools[J]. Applied Mathematics and Mechanics, 1981, 2(6): 679-688.
[20]	Chien Wei-zang. Finite Element Analysis of Axisymmetric Elastic Body Problems[J]. Applied Mathematics and Mechanics, 1980, 1(1): 25-35.